What would a valid "boot sector" for a non-bootable MS-DOS disk be?

Sector 0 of MS-DOS formatted disks generally start with a relative JMP instruction usually followed by NOP (e.g., EB 3C 90), and end with the magic number 55 AA in bytes 511 and 512.

But now I wonder: Was there any kind of "Boot sector" for non-bootable disks? So that if I have my BIOS Boot order set to "A:,C:" and have a disk in the drive, the BIOS will boot from the hard drive instead?

I'm assuming MS-DOS 5.0 on an IBM-Compatible 386-era system, with a FAT12 formatted 3.5" HD 1.44 MB Disk (80 tracks, 18 sectors/track, 2 sides = 2880 sectors of 512 bytes each)

I tried looking at various disk images and even formatted a disk image in MS-DOS running in 86-Box, but they all have a boot sector of sort containing the magic bytes, references to IO.SYS and MSDOS.SYS (even though the actual files aren't on the disk because I didn't format with the "Add system files" option).

I don't remember if any of my PCs at the time did allow booting from hard drive if the floppy disk wasn't bootable (but set as boot priority), so I wonder if this is even possible, and if not then I wonder if there is a free/libre boot sector implementation that does that (without needing a second-stage loader on the disk).